Defending the right of Americans to move in and take over areas where they hadn't lived before, even if someone else claimed it first.
While I'm not about to refight history, one could argue that the other side of the American story might be titled "Not Yours to Take".

If one defines "the general welfare" as the welfare of all the people; and if one returns to the Declaration's triad of "life, liberty and the pursuit of happiness" as a statement of the American mission, as the Constitution is an operational document rather than a mission statement; and if one accepts that these documents, in their writing, listed things in order of their importance (a common practice when interpreting our founding documents), then one can clearly see that "life" is more important than "the pursuit of happiness" because life is a precondition for everything else.

"Life" means food, clothing, shelter and safety (I put medical assistance in this last category). "The pursuit of happiness" can mean the right to be left alone, working to get a good education, the right to worship or not where you please, or it can mean buying everything your neighbors have. "The pursuit of happiness" can't be nailed down at all. "Life" has its hard cases, but is mostly straightforward. The general welfare is best served by making sure that the conditions of life are accessible to all the people, so they may then practice the ways of liberty and pursue happiness, however profoundly or trivially they see it, as well as they are able.

One other thing: mip is correct to look at the verbs. The Constitution says "promote the general welfare". To promote is to make possible, not "to provide", which means to give or hand over, more or less. The only thing the Preamble talks about providing for is the common defense, a recognized function of government since the village council organized guards to keep the leopards out of the livestock.

To promote, though, does mean to create conditions so that what is necessary to the general welfare is readily available to the people. Food, clothing, shelter, and safety should not be priced out of reach for the people, even if that means that those who wish to pursue happiness by amassing enough wealth to buy Connecticut have their happiness somewhat frustrated. Life is a condition. Happiness is a pursuit.

The list of verbs in the Preamble includes, as number two, "to establish justice". The United States is not a culturally based nation, but a nation of laws, contracts and agreements. After establishing the Union, establishing justice was the most important thing, even before defense and the common welfare, because without justice we have nothing to defend and no common welfare to speak of. We need to work on that after the last eight years.